You can have both Java 1.6 and 1.7 installed, but LW requires that 1.6 is the default version. ie: go to your Java Control Panel, set Java (6) 1.6 to be the main version.
At this point, it seems LW 5 will not run with Java 1.7. But 1.7 is not yet the main Java download, so perhaps it's still in beta, anybody's guess.
Just one other point, for Windows 7, Java must be set to Run as Administrator for LW. Two ways to do this, easiest is to right-click the Java 1.6 installer & set to Run as Admin. The other way is tricky, you need to find the actual Java program and find which is the right one to choose.
This post describes how to find the Java program: Solved: "java not found" during LimeWire installation